Experiments with Tandem Planes

The Pendulum Swings again: A Mathematical Reassessment of Galileo’s Experiments with Inclined Planes

After over 300 years of scrutiny, the subject of Galileo continues to be pursued with unabating intensity. Dava Sobel’s Galileo’s Daughter points to the popular interest in the man and his legacy. The Catholic Church, understandably interested in dispelling the notion that its censure of Galileo centuries ago is proof positive that religious faith and science as well as ecclesiastical authority...

TanDEM-X: First Scientific Experiments during the Commissioning Phase

In this paper new and innovative techniques during the commissioning phase of TanDEM-X will be presented that are firstly demonstrated on a satellite platform. The focus is on the secondary goals of TanDEM-X that are assigned for the third year of the mission time life due to the tight schedule for the acquisition of the highly accurate global digital elevation model. Therefore, a variety of sc...

Minkowski Planes with Miquelian Pairs

Generating Discrete Planes with Substitutions

Given a finite set S of unimodular Pisot substitutions, we provide a method for characterizing the infinite sequences over S that allow to generate a full discrete plane when, starting from a finite seed, we iterate the multidimensional dual substitutions associated with S. We apply our results to study the substitutions associated with the Brun multidimensional continued fraction algorithm.

Manifolds With Many Hyperbolic Planes

We construct examples of complete Riemannian manifolds having the property that every geodesic lies in a totally geodesic hyperbolic plane. Despite the abundance of totally geodesic hyperbolic planes, these examples are not locally homogenous.